Abstract
Convergence of powers of a fuzzy matrix has been studied in the literature. In this paper, we shall extend the scope to the products of a finite number of fuzzy matrices. We shall demonstrate that the outcomes of products of fuzzy matrices will be more complicated than the cases of powers of a fuzzy matrix. Two notions of convergence are established: weak convergence and strong convergence. The main results to guarantee the weak convergence of products of fuzzy matrices are due to the concepts of transitive and compact properties of fuzzy matrices, which can be viewed as a generalization of the transitive and compact properties of a fuzzy matrix. Sufficient conditions similar to the pinching theorem in Calculus are given as well for strong convergence.
| Original language | English |
|---|---|
| Pages (from-to) | 203-207 |
| Number of pages | 5 |
| Journal | Fuzzy Sets and Systems |
| Volume | 121 |
| Issue number | 2 |
| DOIs | |
| State | Published - 16 07 2001 |
| Externally published | Yes |
Keywords
- Compactness
- Convergence of products of fuzzy matrices
- Fuzzy matrices
- Transitivity